GCD of Many Integers
نویسندگان
چکیده
A probabilistic algorithm is exhibited that calculates the gcd of many integers using gcds of pairs of integers; the expected number of pairwise gcds required is less than two.
منابع مشابه
Two Fast Parallel GCD Algorithms of Many Integers
We present two new parallel algorithms which compute the GCD of n integers of O(n) bits in O(n/ logn) time with O(n) processors in the worst case, for any ε > 0 in CRCW PRAM model. More generally, we prove that computing the GCD of m integers of O(n) bits can be achieved in O(n / logn) parallel time with O(mn ) processors, for any 2 ≤ m ≤ n/ logn, i.e. the parallel time does not depend on the n...
متن کاملAttack on Fully Homomorphic Encryption over the Integers
Received Jul 17 th , 2012 Accepted Aug 26 th , 2012 Recently, many fully-homomorphic encryption schemes have been constructed. However, the issue of the security of these fully homomorphic encryptions has not been carefully studied. By using lattice reduction algorithm, we firstly present an attack on the fully homomorphic encryption based on approximate GCD over the integers. Our result shows ...
متن کاملOn Silverman's conjecture for a family of elliptic curves
Let $E$ be an elliptic curve over $Bbb{Q}$ with the given Weierstrass equation $ y^2=x^3+ax+b$. If $D$ is a squarefree integer, then let $E^{(D)}$ denote the $D$-quadratic twist of $E$ that is given by $E^{(D)}: y^2=x^3+aD^2x+bD^3$. Let $E^{(D)}(Bbb{Q})$ be the group of $Bbb{Q}$-rational points of $E^{(D)}$. It is conjectured by J. Silverman that there are infinitely many primes $p$ for which $...
متن کاملApproximate Polynomial GCD over Integers with Digits-wise Lattice
For the given coprime polynomials over integers, we change their coefficients slightly over integers so that they have a greatest common divisor (GCD) over integers. That is an approximate polynomial GCD over integers. There are only two algorithms known for this problem. One is based on an algorithm for approximate integer GCDs. The other is based on the well-known subresultant mapping and the...
متن کاملGCDHEU: Heuristic Polynomial GCD Algorithm Based on Integer GCD Computation
A heuristic algorithm, GCDHEU, is described for polynomial GCD computation over the integers. The algorithm is based on evaluation at a single large integer value (for each variable), integer GCD computation, and a single-point interpolation scheme. Timing comparisons show that this algorithm is very efficient for most univariate problems and it is also the algorithm of choice for many problems...
متن کامل